I recently mopped the wooden floor after vacuuming and there were still black "things" and hairs, just more smeared around the room and now wet which made it harder to suck them in with a vaccum cleaner so I had to use kitchen towels anyway. What's the catch behind mopping? Is there a technique that I need to follow? It's honestly the hardest chore for me because it seems to make things worse. The mop head does not detach from the shaft so it's kind of dirty from previous times too and putting it in water barely helps.

Please give tips. I don't really have any other issues with housekeeping except floors and dust cleaning from the shelves because I never had to do it before.

Is it okay to just use wet towels for shelves and floor only? It's more expensive because you have to buy a lot extra and my mom does it with cloth but I don't want to ask her because we aren't on the best terms.